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## Creation of Plausible Values

After obtaining marginal maximum likelihood estimates of parameters, and Σ, of in the population structure model (denoted by and ), twenty sets of plausible values, denoted by θm (m = 1,2,…,20), for all sampled respondents are drawn in the following three-step process.

1. A vector or a matrix m is drawn from the distribution of as estimated using the population-structure model,

where x, is the item response matrix, y is a matrix containing group membership information, is the matrix for item parameter estimates, and is the estimated covariance matrix in the population structure model.

2. Conditional on the generated value m, and the fixed value , and the fixed value , the mean vector and the covariance matrix for the predictive conditional distribution of respondent r are computed from the predictive conditional distribution

3. Finally, a multivariate plausible value is drawn from a multivariate normal distribution with mean vector and covariance matrix

These three steps are repeated twenty times producing twenty sets of plausible values for all sampled respondents.

Last updated 02 June 2016 (GF)